The average height of humans is not a constant number. It varies throughout history and dependent on gender and race. Periods of abundance in food usually resulted a growing average height in upcoming generations.
Beethoven lived from 1770 to 1827. In this period an average European male was 160-170 cm tall (5’3-5’7).
Unfortunately, we do not have written evidence on Beethoven’s height. We know from testimonies that both his parents were described as tall. Fischer, a family friend, described Madame van Beethoven as “rather tall”. His father, Johann, was remembered by Frau Karth (a neighbor) as “a tall, handsome man with powdered head”. What is tall, we do not know exactly!
To the question, how tall Beethoven was, it is not possible to give a definitive answer. Most sources portray him as average height, definitely not short or tall. If so, he must have been around 165 cm (5’4) tall.
More on Beethoven’s appearance here!